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प्रश्न
The regression coefficient of Y on X
पर्याय
bxy = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)`
byx = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dy"^2 - (sum"dy")^2)`
byx = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`
bxy = `("N"sum"xy" - (sum"x")(sum"y"))/(sqrt("N"sum"x"^2 - (sum"x")^2) xx sqrt("N"sum"y"^2 - (sum"y")^2))`
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उत्तर
byx = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`
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संबंधित प्रश्न
The heights (in cm.) of a group of fathers and sons are given below:
| Heights of fathers: | 158 | 166 | 163 | 165 | 167 | 170 | 167 | 172 | 177 | 181 |
| Heights of Sons: | 163 | 158 | 167 | 170 | 160 | 180 | 170 | 175 | 172 | 175 |
Find the lines of regression and estimate the height of the son when the height of the father is 164 cm.
The following data relate to advertisement expenditure (in lakh of rupees) and their corresponding sales (in crores of rupees)
| Advertisement expenditure | 40 | 50 | 38 | 60 | 65 | 50 | 35 |
| Sales | 38 | 60 | 55 | 70 | 60 | 48 | 30 |
Estimate the sales corresponding to advertising expenditure of ₹ 30 lakh.
Find the equation of the regression line of Y on X, if the observations (Xi, Yi) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).
A survey was conducted to study the relationship between expenditure on accommodation (X) and expenditure on Food and Entertainment (Y) and the following results were obtained:
| Details | Mean | SD |
| Expenditure on Accommodation (₹) | 178 | 63.15 |
| Expenditure on Food and Entertainment (₹) | 47.8 | 22.98 |
| Coefficient of Correlation | 0.43 | |
Write down the regression equation and estimate the expenditure on Food and Entertainment, if the expenditure on accommodation is ₹ 200.
The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.
If X and Y are two variates, there can be at most
The lines of regression of X on Y estimates
If the regression coefficient of Y on X is 2, then the regression coefficient of X on Y is
Using the following information you are requested to
- obtain the linear regression of Y on X
- Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82
∑X = 424, ∑Y = 363, ∑X2 = 21926, ∑Y2 = 15123, ∑XY = 12815, N = 10.
Here X is the expenditure on inspection, Y is the defective parts delivered.
The following information is given.
| Details | X (in ₹) | Y (in ₹) |
| Arithmetic Mean | 6 | 8 |
| Standard Deviation | 5 | `40/3` |
Coefficient of correlation between X and Y is `8/15`. Find
- The regression Coefficient of Y on X
- The most likely value of Y when X = ₹ 100.
